Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in OLG Models

Speaker
Anna Rubinchik, Western Galilee College
Date
29/03/2022 - 13:00 - 11:30Add To Calendar 2022-03-29 11:30:00 2022-03-29 13:00:00 Necessary and Sufficient Conditions for Determinacy of Asymptotically Stationary Equilibria in OLG Models We propose a criterion for verifying whether an equilibrium of an overlapping generation model is amenable to local policy analysis, i.e., is determinate. The criterion is applicable for a generic set of parameters of the model, and in case of indeterminacy, it indicates the nature of the problem: multiplicity of equilibria or their absence for near-by parameters. The criterion can be applied to models with infinite past and future as well as those with a truncated past. The baseline equilibrium is not required to be a steady state, and economic parameters, for example endowments, can change over time. However, asymptotically, the equilibrium should be stationary, though the two limiting paths at either end of the time-line do not have to be the same. If they are, conditions for local uniqueness of equilibrium are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past. We illustrate our main result using a text-book model with a single physical good and a two-period life-cycle. In this model our criterion is used to identify the three possible cases: determinacy, and hence, local uniqueness,  and indeterminacy: multiplicity and non-existence of equilibria in the neighbourhood of the baseline. Joint with A. Gorokhovsky, CU Boulder Links to the paper and the seminar recording. BIU Economics common room and will be Zoomed on https://us02web.zoom.us/j/82536086839 אוניברסיטת בר-אילן - Department of Economics Economics.Dept@mail.biu.ac.il Asia/Jerusalem public
Place
BIU Economics common room and will be Zoomed on https://us02web.zoom.us/j/82536086839
Affiliation
https://sites.google.com/view/annarubinchik/home
Abstract

We propose a criterion for verifying whether an equilibrium of an overlapping generation model is amenable to local policy analysis, i.e., is determinate. The criterion is applicable for a generic set of parameters of the model, and in case of indeterminacy, it indicates the nature of the problem: multiplicity of equilibria or their absence for near-by parameters.

The criterion can be applied to models with infinite past and future as well as those with a truncated past. The baseline equilibrium is not required to be a steady state, and economic parameters, for example endowments, can change over time.

However, asymptotically, the equilibrium should be stationary, though the two limiting paths at either end of the time-line do not have to be the same. If they are, conditions for local uniqueness of equilibrium are far more stringent for an economy with a truncated past as compared to its counterpart with an infinite past.

We illustrate our main result using a text-book model with a single physical good and a two-period life-cycle. In this model our criterion is used to identify the three possible cases: determinacy, and hence, local uniqueness,  and indeterminacy: multiplicity and non-existence of equilibria in the neighbourhood of the baseline.

Joint with A. Gorokhovsky, CU Boulder

Links to the paper and the seminar recording.

Last Updated Date : 30/03/2022